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Stability of RNA hairpin loops: A6-Cm-U6
J. Mol. Biol. (1973) 73, 483496
Stability of RNA Hairpin Loops : A~-Cm-U, OLKE
C. U~ENBECE~,
PHILIP N, BORER, BARBARA IISNACIO !I’INOCO JR
DEN~LER
AND
Department of Chemistry University of California Berkeley, CaliJ’, 94720, U.S.A. (Received 17 April 1972) The thermodynamics and circular dichroism of a series of A&,-Us (m = 4, 5, 6 or 8) oligoribonucleotides have been studied. These molecules form intramolecular hairpin loops at low temperatures and therefore are useful models for similar structures which occur in larger, natural RNA molecules. The stability of the helix forming the stem of these loops was found to be considerably greater than an intermolecular helix with the same length and composition. The most stable loop is m = 6. The enthalpy for initiation of the loop is unfavorable; it ranges from + 24 kcal. for m = 4 to + 21 kcal. for m = 0. The maximum in stability for the Cs loop and the large positive enthalpy for loop initiation are in disagreement with expectations from simple theories assuming a Gaussian distribution of end-to-end distances. Loop strain for m = 4 and m = 5 and the unstacking of the cytosines on loop formation are likely physical explanations for these thermodynamic data. The circular dichroism spectrum of cytosine residues in the Cs and Cs loops is very similar to the spectrum of single-stranded oligoribocytidylate. However, the cytosine residues in the Cs loop have a very different circular dichroism spectrum from the corresponding oligo(Cs) spectrum. ‘Tu accordance with the thermodynamic data, we conclude from the circular dichroism data that the Ce loop has an altered conformation from the C, and c,$ loops.
1. Introduction loops are a necessary feature of RNA secondary structure. Whenever an antiparallel helical region is formed by base pairing between complementary sequences of an RNA strand, a hairpin loop must be formed as well. One expects the loop to stabilize its intramolecular helical region relative to an identical intermolecular helix. However, in order accurately to predict a secondary structure on the basis of sequence (Kallenbach, 1968 ; Tinoco, Uhlenbeck & Levine, 1971; DeLisi & Crothers, 1971) it is necessary to have precise thermodynamic information about loop stability. Very few thermodynamic data on loops are presently available. Scheffler, Elson & Baldwin (1970) have studied loops formed by deoxy(A-T) oligomers of various lengths. Loops have also been obtained as fragments of transfer RNA molecules (Romer et al., 1969; Coutts, 1971). It has been difficult to determine from these data (1) the amount which a loop stabilizes its helix and (2) the effect, of the number of residues in the loop on the stability of the helix. In this paper, RNA oligomers of the form A&$,-Us (m = 4, 5, 6 or 8) are studied. It is established that these molecules do indeed form hairpins with a helix of six A-U base pairs and m. cytidine residues in the loop. The thermodynamics of loop Hairpin
t Present 1-.S.A. 33
address:
Department
of Biochemistry, 483
Universit’y
of Illinois,
Urbana,
Ill.
61801,
484
0.
C.
UHLENBECK
ET
AL.
initiation are determined and found to be very different from expected values. The circular dichroism spectra of these molecules also give information about the conformation of the C residues in the loop.
2. Materials and Methods The (A~)~A(pc),,,(pu), oligomers (A&,-U,) were synthesized enzymatically in three steps. First, poly(A) was hydrolyzed, the terminal phosphates were removed with alkaline phosphatase, and the oligomers were separated to obtain A,; second, C residues were added to the 3’ end of As with primer-dependent polynucleotide phosphorylase and the different A&&, oligomers separated; and third, U residues were added to each A-C block copolymer and separated again. The conditions for the f&t two steps were identical to those described by Martin, Uhlenbeck & Doty (1971) for the synthesis of A,-TJ,, except that CDP was used instead of UDP. The addition of U residues to A&&,, was done under the following conditions: 0.54 mM-As-C,, 17 mM-[3H]UDP (5.7 Ci/mole), 0.01 M-MgCl,, 0.6 an-NaCl, 0.2 M-&C&! buffer (pH 9.3) and 0.3 mg/ml. concentration of primer dependent polynucleotide phosphorylase from M. luteua. The reaction was run at 37°C for 2 hr. Unfortunately, the A& reaction mixture was lost and has not been repeated yet. Reaction products were separated on a 50-ml. TEAE-cellulose column at pH 3.5 in 7 M-urea. The reaction mixture was diluted with 7 M-urea to an ionic strength of 0.02 M and applied to the column at neutral pH. The unreacted UDP was usually eluted from the column with 0.05 M-Nacl, 0.01 rd-Tris in 7 M-Urea at pH 8. Then the column was equilibrated with 0.01 M-sodium formate, 7 M-urea (pH 3.5) and the oligomers were eluted with a gradient (900 ml. total volume) from 0 to 0.275 M-NaCl in 0.01 m-sodium formate, 7 M-urea (pH 3.5). The elution profile for A&&-UN is shown in Fig. 1. Fractions were pooled and desalted as described in Martin et al. (1971). Identification of the reaction products was accomplished by two methods. First, the specific activity of each peak could be compared with the fraction of U residues in the molecule and second, early peaks could be hydrolyzed with RNase A, chromatographed on paper to separate U and Up, and the radioactive Up/U ratio determined, thus giving the chain length (Martin et al., 1971).
Bm. 1. TEAE-cellulose colunm elution profile of A&U, oligomeru. The large first peak (2) contains N = 0, 1 and 2 as well as some of the UDP. The succeeding peaks me the A,C,UN series starting with N = 3. (SW text for chromatogmphic details.)
STABILITY
OF RNA
HAIRPIN
LOOPS
486
(b) Measurements Absorption-temperature profiles were measured on an automatic recording spectrophotometer (Gilford Instruments) es described in Martin et al. (1971). The solvent consisted of 1 M-NaCI, 0.01 ~-sodium phosphate buffer, and lo-* M-sodium EDTA, adjusted to pH 7. Ultraviolet absorption spectra were obtained with a Gary no. 14 spectrophotometer equipped with a thermostatically controlled circulating block. Circular dichroism spectra were taken with a Cary no. 60 spectropolarimeter with a model 6001 accessory. A PDP S/S computer wae used for on-line data acquisition and reduction (Tinoco & Cantor, 1970). The temperature was controlled by a thermostatically controlled thermoelectric cooler (Allen, Gray, Roberts & Tinoco, 1972). The spectra are presented ae either circular dichroism (cn - cs) or ellipticity per mole of base. Extinction coefficients were obtained by alkaline hydrolysis of the oligomer. The values obtained for l zeo at 47% of A&&-Us are 9.3, 9-3, 9.1, 9.0 ( X 103) lmole-lcm-l for m = 4, 5. 6 or 8, respectively. (c) Treatmerrt of melting d&u The absorbance-temperature profhes of the loop to coil transitions of the A&&-U, oligomers represent a sum of (1) the change in absorbance of the A*U double helix melting; (2) the change in absorbance of the C residues se the loop becomes a single strand; and (3) the change in absorbance of the single strand with temperature. It is therefore not possible to evaluate the absorbance-temperature profile ae a helix-oil transition unless certain assumptions and corrections are made. Figure 2 summarizes the conversion of a melting curve to a plot of fraction helix verau.s temperature. The melting curve, A(T), can be corrected for single-stranded unstacking by using the absorbance change accompanying this unstacking, A,(T), as the upper bound of the melting curve (Martin et al., 1971 and Fig. 2(a)). As(T) can be measured by melting at very low salt ooncentrations, where no helix is formed or it can be calculated from the unstacking of the component residues. The absorbance of the fully formed loop, A,(T), is more diflicult to obtain. In all the loops studied, the transition was quite broad and occurred at such low temperatures that
Temperature
(“Cl
FIQ. 2. (a) Absorbance-temperature profile of AB-C&-U6 in 1 n-N&l, 10 mn-sodium phosphate (pH 7) normalized to 1.0 at 60°C and an average of five different concentrations. A,(T) is the absorbanoe of the oligomer as a single strand. AD(T) is the absorbanoe of the fully formed loop extrapolated to 0 slope in method 1 and to a slope corresponding to oligo (C) unstaoking in method 2. (b) Fraction of loop vef%?u8 temperature for A~-CB-UBcalculated from (a) by methods 1 and 2.
486
0.
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-11,
at 0°C the loop was uot fully formed. Thus, A,(T) must be obtuiuod by extrapolation. Furthermore, since the conformation of the C residues within a closed loop may change with temperature, A,(T) might change with temperature. In order to obtain a reliable estimate of AL(T), the slope of A(T) is plotted as a function of temperature and extrapolated to low temperature. One can extrapolate to zero slope and choose A,(T) as independent of temperature and equal to the extrapolated absorbance. This is method I shown in Fig. 2. Alternatively one can assume that the C’s in the loop change their absorbance with temperature as much as single-stranded oligo (C) does. In this case (method 2) A,(T) is extrapolated to a final slope of O.2o/o/1O deg. C. For both methods, the frection of loop, f, is then calculated as :
43(T) - A(T) f = A,(T) - A,(T). In Fig. 2(b), f ver8u9 T is given for the two alternative methods of estimating A,(T). Only a few degrees difference in the T, (f = 0.5) and a small change in the slope is observed. We will baee the results on method 1, a constant value of AL( T), for simplicity. An alternate method of evaluating T, is to equate it to the maximum in slope of the measured absorbance (dA/dT) max. This method led to higher values of T, than reported here. However, it did not give an internally consistent pattern of results and there is no theoretical reason why the maximum in slope of absorbance should occur at f = O-5 for a multistep equilibrium.
3. Thermodynamic
Results
(a) Single strand to complete loop We want to study the thermodynamics of formation loops. The complete reaction can be written as A,-C&U,
(single strand) + A&&-U,
of intramolecular
hairpin
(loop)
with equilibrium constant equal to f/( 1 - f) where f is the loop fraction. The thermodynamic parameters which characterize the reaction are : T,, the temperature where f = 0.5 (the equilibrium constant = 1); AH0 (total), the standard enthalpy of the reaction; AX0 (total), the stands,rd entropy of the reaction. The value of AH0 (total) can be derived from the van? Hoff equation.
AH0 (total) = 4RT& (aflaT),,.
(1) This form is used because the value of the slope (aflaT) is most accurate at T, where it is least affected by assumptions about extrapolated low and high temperature values for absorbance. This relation will underestimate the value of the total enthalpy if the reaction is not a two-state equilibrium as shown. The standard free energy, AGO,equals 0 at T,, so the standard entropy is given by:
AS0 (total) = AH0 (t&1)/T,.
(2)
Since both the loop to single strand transition and the unstacking of single strands are intramolecular reactions, the absorbance versus temperature profiles of the loops should be independent of concentration. Thus, for each A,-C,-Us (m = 4, 5, 6 or 8) at least four absorbance veTsu.9T curves were obtained over a 25-fold range of oligomer concentration. In each case, the normalized absorbance curves were independent of concentration to within experimental error. We concluded that only intramolecular loops formed and we averaged the data for the different concentrations. Further evidence for the formation of double-stranded intramolecular helices came
STABILITY
I 01’
OF
RN.4
H.1IRI’IN
-.------
b
-10
IO
LOOT’S
20
30
Temwrotwe
40
i
b0
5G
(“Cl
FIG. 3. Loop fraction vws’8u8temperature for As-&,-Us wz == 4,5,6 or 8 in 1 M-NaCl, 10 mm-sodium phosphate (pH 7) calculated by method (1). Each curve is an average of at least four different oligomer concentrations. The dotted lines indicate extrapolation of low temperature data.
from the ultraviolet spectra of the loops. The spectral changes on melting of A,C,-U, were consistent with double-strand melting, while for oligomers with more than six uridines, the spectral change is characteristic of triple-strand formation, suggesting multistrand aggregates (Martin et al., 1971). If the absorbance of the completely formed loop is assumed to be independent of temperature (method l), the f versus T curves thus obtained for the four oligomers are shown in Figure 3. The thermodynamic parameters obtained from these curves are given in Table 1. (b) Loop initiation To learn about the process of closing the loop by the formation of the first base pair, we must consider the single strand to loop reaction in more detail. The simplest TABLE 1
Experimental thermodynamic parameters for the reaction A,&‘,,,- U, (sin~glestrand) to A,-C,-U, (loop) Loop
Tm (“‘3
&CaUfi
2 13.4 21.0 13.4
A&Us AeCeU, AeCsUe t The percentage
AH0 (total) (kcal./mole)
is calculated
O/h = 1oo x As (SO’C) - AL (--10°C) 0
As(60"C)
‘WI
(4 -- 44 -46 -54 -61
-12 -13 -16 -14
hyperchromioity
ASP (total)
17 19 17 19
at 60% as
*
0.
488
C. UHLEKBECK
E’T
AL.
(all or none) assumption is that the reaction takes place in one step, and that the equilibrium constant for the reaction of A,-C,-U, can be written as f y-q
=
YllP
N-l
where y,,, is the equilibrium constant for loop initiation for a loop of VL unbonded bases and s is standard notation for the equilibrium constant for adding each successive base pair to an initiated helix. Both s and Y,,, are expected to be temperature dependent. s(T) = exp [-(dRO/R)(g
24&J
= ymWexp
- &)I
[--(dH9IR)(~
,
- $1
.
In the equation for s(T), Tz is defined as the temperature where s = 1. For the A-U base pairs in A,-C,-U, this is equal to the T, for poly(A)*poly(U) at the same salt concentration. The standard enthalpies which appear in the equations are: AH,O, enthalpy of loop initiation, and Al?O,enthalpy (per base pair) of helix propagation. For simplicity the enthalpies are chosen independent of temperature, although in general they should also vary with temperature. Applying the van% Hoff equation, that is, taking the derivative of the equilibrium with respect to temperature, we obtain
1
1
R (N - l)AHi” In Ym(Tm)
for the relation between melting point for the loop, T,, and thermodynamic parameters. This equation differs from that given by Kallenbach (1968) by the appearance of (N - 1) instead of N. He chooses the equilibrium constant for loop initiation to be proportional to a; this leads to (N)Al?O. We follow Scheffler et al. (1970) in the definition of ym; they discuss its advantage. Tg and AR0 can be obtained directly from experiments on poly(A).poly(U). AR0 can also be calculated from thermodynamic data on the melting of self complementary oligomers of the type A,-U,. In 1 M-N&~ we use: Tz = 78°C and AR0 = -8.0 kcal./mole (Tinoco et al., 1971). When these values and the measured T, for each oligomer are substituted into equation (4), one obtains y,,, values for the four loops at their T,. The enthalpy of initiation, AHlo, for these oligomers can be obtained by subtracting (5)( -8.0) = -40 kcal./mole from the enthalpy of the total reaction given in Table 1. AHi can then be used to calculate y,,, at 26°C from y,,, at T, by equation (3). The y,,, (25°C) and the corresponding free energies and entropies of initiation at 25°C are given in Table 2. Data are also available for a loop with an altered stem (C. Cech, unpublished work). The loop formed by As-G-C&-U, is similar to the A,-C!,-Us loop except that the base pair closing the four rmbonded cytosines is a G*C pair instead of an AmU pair. The T, of As-G-C&-U, is 19.7% and its total AH0 = -15 kcal./mole. The fact that this T, is nearly 18 deg. C higher than the T, for A,-C,-U, is not surprising in view of the fact that the A,-G-C&-U, stem contains 16.7% G-C base pairs. Using equation (4) with Tg adjusted to 90°C to account for the higher G-C content, we obtain y,,,
STABILITY
OF RNA
HAIRPIN
489
LOOPS
TABLET Calculated thermodynamic parame&rs at 25°C for form&q the jirst A- U base pair which chxes a loop of C residues All-or-none No. of bases in loop (m) 4 5 6 8
Ym
0*7x 1.6 x 2.6x 1.4x
10-e 10-e 1O-5 10-S
model
AH,O (kcal./mole)
AS,0 (eu)
AB,O (kcal./mole)
+2s
+70 +@J +59 +65
+7*1 +6.6 +tG3 +6*6
+27 +24
+26
Model with intermediate No, of bases in loop (m) 4 5 6 8
Ym
0.3 x 0.9 x 2.0x 1.1 x
10-B 10-s 10-5 10-E
states
AH,O (kcal./mole)
AS,O (eu)
A&O (kcal./mole)
+24 +24
1-55 -1-57 +49 -t 68
+7*5 $6.9 +6.4 $6.8
+21 +24
(25’C) = 0.5x 10-5, AC,0 = $7.3 kcal., ARio = $25 kcal. and AS,0 = +59 eu. These values are very similar to those given in Table 2 for A6-C4-U6. Up to this point, the thermodynamics of loop formation has been discussed in terms of a simple two-state model. Although it seems intuitively reasonable that this approximation is valid for loops containing only a few base pairs, it is important to test the validity of the approximation by computing the thermodynamics with a more rigorous model. Thus, a partition function which contains all the likely partially bonded intermediate states was derived; the contribution of each intermediate state to the absorbance was assessed; and the effective fraction of base-paired states was calculated (M. D. Levine, unpublished work). In this formulation, a statistical weight of 1 WESassigned to the single strand. All possible loop sizes were considered for the partially bonded states. That is, for A,-C,-U, loops of m, m + 1, m + 2 . . . m + 2N - 2 unbonded bases were counted as intermediate forms. In other words, not only could melting occur from either end of the helix, but staggered conformations with tm uneven number of A’s and U’s in the loop were allowed. However, interior loops and “bulges ” in the helix were excluded as they can easily be shown to be negligible for a helix which can at most contain six base pairs. The contribution of each intermediate state to the change in absorbance was assumed to be proportional to the number of base-pair stacking interactions. A nearest-neighbor approximation of this sort has been found to be applicable in many related contexts (Gray & Tinoco, 1970). The effective fraction of base-paired states could then be calculated as a function of temperature with y,,, and AHi as variable parameters. AB” was chosen equal to -8-O kcal., as before. Unlike in the all-or-none model, the parameters for each oligomer depend on all the other oligomers. For example, to calculate a melting curve for A&&-U, all possible loop sizes from the minimum loop of four unbended bases to the maximum loop of 14 unbonded bases must be considered. That is, the
490
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AL.
values of y4, ys . . . y14 must all be specified. However, in this case, t,he most important variable is y4 corresponding to the actual number of residues in the fully formed loop. The other values of y,,, are used to calculate the intermediate, partially paired forms. Values of y,,, for m > 8 were calculated from Ys+s
-=
9
a/=
( 9t-2 > * This is the chain-length dependence for ym predicted for a single strand which has a Gaussian distribution of end-to-end distances (Jacobson & Stockmayer, 1950). The values for AH,O for m > 8 were set equal to AH,O(m = 8). y7 and AH,O(m = 7) were chosen as the average of the corresponding values for m = 6 and m = 8. The values of the thermodynamic parameters at 25°C obtained from fitting the calculated values (by the complete partition function) of T, and (df/dT) Tmto the measured values are given in Table 2. The values are not too different from those obtained from the all-ornone model; however, the partition function shows that intermediate species are significant. This is particularly true for A&,-U, and A&,-U, where one base pair can break to produce a more favored loop. Y8
4. Thermodynamic
Discussion
The best way to discuss the results of the thermodynamic analysis of loop closure is in the context of what one should expect. For a flexible chain the probability of loop closure should increase as the chain length decreases. Ideally, this should continue until some minimum loop size is reached. Since model building indicates that the minimum loop size is three unbonded bases for polyribonucleotides, we expect y,,, to increase as m decreases, with y3 a maximum. The simplest theory of loop initiation based on a “random coil ” single strand (Jacobson & Stockmayer, 1950) predicts in fact that y,,, should be proportional to (m + 1)-3Ja. The only previously measured value for ym is that of y4 = 30 x 10m5by Scheffler etal. (1970) for deoxy(A-T) oligomers in 0.5 M-Na + . They assumed that the value was independent of temperature, that AHi was zero. It does indeed seem reasonable for AH,O to be zero or plus or minus 1 or 2 kcal., if the enthalpy of initiation is a result of forming two hydrogen bonds (one base pair) in aqueous solution in a completely flexible loop. The experimental thermodynamic results are gathered in Tables 1 and 2. We immediately note that the measured T, values, and therefore the calculated yrn values, do not increase monotonically with decreasing numbers of C’s in the loop. Although the T, for the CC loop is greater than that of the C, loop, the T, values of the C4 and C, loops are less than the C, loop instead of more. Furthermore, the value of y4 calculated with the complete partition function is l/100 the value of y4 for the deoxy(A-T) oligomers. The ym values are also very temperature dependent; the AHi values are over 20 kcal. Finally, the free energies of initiation, which range from f7.5 to +6*4 kcal./mole are somewhat higher than expected (Tinoco et al., 1971; DeLisi & Crothers, 1971). However, DeLisi & Crothers (1971) did calculate that a loop of five unbonded bases should be slightly more stable than one of four unbonded bases. It is also rather remarkable that the ASi displayed in Table 2 have such large positive values. The large entropy increase upon forming a more ordered structure apparently reflects a favorable change in wat,er structure.
STABILITY
OF RNA
HAIRPIN
LOOPS
491
The discrepancy between the measured values and trends for AG,O, AH,0 and AX,O and the simple theoretical estimates can be attributed partly to unstacking of cytosines when the single strand is bent into a loop. If the temperature dependence of the optical rotation of CpC is analyzed in terms of a two-state stacked or unstacked model, approximate values of AH0 (unstacking) = +7 kcal. and AS0 (unstacking) = 25 eu are obtained (Davis & Tinoco, 1968). Therefore, independent of the size of the loop, the values of AHi and AXi in loop initiation are consistent with loss of about three CpC stacking interactions. Thus, either all the cytosines in the loop are partially unstacked or two cytosines are completely unstacked. Studies with molecular models of loops with four to eight unbonded bases indicate that both these possibilities could occur. A model of a loop of seven residues in which two of the bases are completely unstacked and the other five are fully stacked has been carefully described by Fuller & Hodgson (1967). These results imply that the stability of a loop can depend on the base composition and sequence of the residues in the loop as well as those which close it. Uracil, which essentially does not stack, should be particularly important. RNA loops with only A, C, or G in them probably show similar behavior to the C-containing loops studied here. Loops which contain U (particularly next to the helical region as in anticodon loops) may have smaller y,,, and AHi values near zero. These loops could be more reasonably compared with the theoretical estimates of AG,O which ignore basebase interactions. The recent work on A,-G-C&U4 hairpin loops by Gralla & Crothers (1973) made us reassess carefully our methods and results. We conclude that our experimental results are essentially consistent with theirs; our analysis is different. We try to est)imate the fraction of loop (f) versus T by making reasonable assumptions about the absorbance of the oligonucleotide. Once f is obtained, our thermodynamic analysis is straightforward and gives T,(f = 0.5) and AG,O, AH,O and AS,O. Gralla & Crothers do not attempt to make assumptions about absorbance. They equate T, to the maximum in the slope of absorbance verse T and they assume that AHi = 0. In an attempt to get agreement with Gralla & Crothers we assumed a very large variation in absorbance of the completely formed loop with temperature A,(T). This led to enthalpies for loop initiation (AH,O) of about $10 kcal. We could not make our data consistent with AH,O = 0.
5. Circular Dichroism The circular dichroism spectrum was measured for each of the A&,-U, as a function of temperature in 1 M-N&I at pH 7. The spectrum of each oligomer at 0°C is shown in Figure 4. However, even at 0°C these oligomers are not all in one conformational form. The fraction of helix varies from 0.54 for A,-C?,-U, to 0.87 for As-C&U,; this makes the spectrum quite complex and difficult to analyze. Thus, the 0°C spectrum is a mixture of the spectra of single strands, of the fully formed loop and, if intermediate states are important (as deduced from the partition function), of loops with incompletely formed helices. When temperature is increased, the proportions of these different forms change and a corresponding circular dichroic spectral change is seen. In Figure 5 the spectrum of A,-C&Us is shown at four temperatures spanning the transition range. As was the case for the absorption-temperature studies, the differences between the low and high-temperature circular dichroism spectra are due to (a) the change due to the A*U pairs breaking, (b) the change due
0.
492
/
i8
C. UHLENBECK I
I
ET
AL.
I
I
I
Wavelength
(nm)
I
I
..‘..“..
A6- C&
fLoop =O-77
---
Ag-Cg-Ug
fLoop =0,87
-- -- - -
A’6-Cg-Us As-L-U6
fL,,p ~0 74 fLoop =0,54
I
(6
I
with m = 4,6,6 or 8 in 1 M-N&I, 10 rnM-sodium FIQ. 4. Circular dichroism spectra of A,-C,-U, phosphate (pH 7) at 0°C. The fraction of fully formed loop (f) for each oligomer is shown in the Figure.
T !61-
I
I
I
-__
14.--I
-61
I
0°C !=087 Q-yCfz, 60°C f q OOl
’
I
220
I
I
240
I
I
Wavelength FIQ.
6. Circular
diohroism
I
260
I 280
I
I 300
I-2
inm!
of A&&U8
at 0, 20,40 and 60°C.
to unstacking of the single strands with temperature, and (c) the change accompanying the unstacking of the C residues when the loop is formed. The circular dichroism spectrum can be used to give qualitative information about the residues in the loop if we assume that the value per base of the A,*U6 stem can be estimated from circular dichroism measurements of double-stranded A*U base pairs. In the simplest method, we assumed that the spectrum of the cytosine residues in a loop can be obtained by subtracting the spectral contribution of the A-U stem from the total spectrum of the loop. The A-U contribution at different values off was obtained from measured circular dichroism spectra of A,-Ue at the same value off. The double helix formed by A,-Us was chosen as a model for the stem region of the
STABILITY
OF RNA
HAIRPIK
LOOPS
493
loop because, as an oligomer, it probably corresponds more closely to the conformation of the stem region than does the double-stranded polymer poly(A) *poly(U). Furthermore, A,-U, melts over a sufficiently wide range to obtain spectra at various values of j. Oligomer mixtures of A, and U, tend to form triple-stranded aggregates in high salt concentrations and thus are not suitable models. We therefore measured the circular dichroic spectrum of an A,-C,-U, loop at various temperatures (corresponding to different j values) and subtracted the correct molar proportion of the A,-U, spectrum measured at the same value of j. In the A,-C,-U, case, the absorbance-temperature profile is similar to that of A,-U, so the contribution of singlestrand stacking to the difference spectrum is quite small. The total contribution of the A-U residues is thus removed from the spectrum even though they are partially paired and partially single-stranded. Single-strand stacking appears more in the subtractions for the other loops since the temperature of the A,-Uc spectrum must be higher for these less stable loops. This difficulty is most serious in the case of A&7,-U, where, for example, an A,-U, spectrum at 25°C (j = 0.54) must be subtracted from the 0°C loop spectrum (f = 054). In Figure 6(a) and (b), the spectrum
1'
-I-, 22 20
/i:
_ (b)
18 16 14 12 IO 8 6 4
Wavelength
( nm i
FIN. 6. Three times the circular dichroism of A&&,-U6 minus twice the spectrum of Ae-U,, at (a) f = 0.87 (OV for loop) and at (b) f = 0.14 (4O’C for loop) compared with the spectra of Cg at 0 and 40°C.
PO.1
0.
C. UHLENHECK
E7’
;il;.
of the cytosines in the C, loop of A&&-U, at O’C are compared with the measured spectra of the oligonucleotide (Cp)& The comparison is made at 0°C and 40°C corresponding to f values of 0.87 and 0.14 for the loop. Three points should be noted. First, there is excellent agreement of the general shape of the calculated spectrum of the C residues in the loop and the measured oligo(C) spectrum. This suggests that the loop C residues are in an average conformation not radically different from what, they are in single-stranded oligo(C). The second point is that the calculated circular dichroic spectra of the C residues in the loop change with temperature, implying t,hat these residues are quite free to move while in the loop. Finally, the intensity of the calculated spectra is always somewhat greater than the corresponding measured oligo(C) at the same temperature. Although this may imply that C’s in the loop have more structure than in the single strand, the many assumptions involved in the subtraction make quantitative conclusions suspect. An attempt to improve the calculation of the spectra of the loop residues was made by assuming nearest-neighbor interactions for the A*U interaction in the center of A,-U, and for the A-C and C-U interfaces between stem and loop. We correct for the fraction of single strand by subtracting an appropriate amount of the circular dichroism of the oligonucleotide C,. This leads to a very similar shape and about a 5% increase in the maximum at 275 nm. Thus, no significant change from the simpler method is obtained. When the calculation of the circular dichroic spectrum of C residues in the loop is made for the other A&,-U, loops, an interesting observation is made. For m = 8 the spectra are essentially the same as for m = 6, but for m = 5 the calculated spectra differ considerably in position and magnitude from the corresponding oligo(C) spectra. Figure 7 shows the contribution of the C residues in the loop for A,-C&-U, and A,-C&-U, at 0°C. These molecules both have about 75O/, helical structure at 0°C and are directly comparable. A similar comparison with the C, loop is not expected to be accurate since A,-C,-U, is only 54% helical at O”C, leading to a large contribution from single-strand stacking in the difference spectrum. The circular dichroism
240
260
280
300
320
Wavelength (m-n)
FIG. 7. Calculated ciroular diohroism spectra of loop cytosines in A@-CS-UB at 0°C (f = 0.77). The appropriate amount of the diohroism of A,-UB at the same fraction helix is subtracted as in Fig. 6.
STABILITY
OF
RNA
HAIRPIN
LOOPS
-195
data imply that the C, loop has an altered conformation from the C6 and C, loops. This is consistent with the anomalously low stability found for C, and C, loops.
6. Conclusion The RNA hairpin loops studied in this paper are of the same size range as those believed to occur in natural RNA’s. Although the sequence of residues in the model loops could not be considered very natural, the information obtained from these molecules is probably quite applicable to their biological counterparts. The stability of the helical region closing the model loops was studied in detail. As was expected, the entropic effect of restraining complementary sequences to be close to one another did much to stabilize the helix. In our case, the T, of two complementary strands with six A.U base pairs has been estimated to be -13°C at 10m4 M strand concentration (Martin et al., 1971), while the T’, of the loops are in the range of +lO”C at all strand concentrations. The most striking result of the stability measurements was that the six-membered loop was the most stable. Smaller loops were strained and larger loops showed the expected decrease in stability due to decreased probability of the A, and U, regions meeting. We note, of course, that two of the three loops in the well-described cloverleaf model of transfer RNA always have seven residues. Unfortunately, we did not measure a loop with seven bases, but we are confident that such a loop will have near maximum stability. Little can be said about the conformation of the residues in the loop. The high free-energy of initiation of the first helix base pair suggests that either total unstacking of two loop residues or partial unstacking of all the residues must occur before the loop can form. This conclusion should be checked with loops which have U residues in them and therefore do not stack well, or with loops melting at higher temperatures in which the loop bases unstack before the loop melts. The circular dichroism studies suggest that the average conformation of the C residues in the unstrained loops is not significantly different from the average single-strand conformation of oligo(C) residues. The measurements are not sensitive enough to confirm the unstacking predicted by the thermodynamics. The average conformation of the C residues in the loop A&,-U, apparently is different from As-Cs-Us, A,-C&-U,, and oligo(C), since the calculated circular dichroism spectrum is considerably different. We expect similar behavior in the C, loop, but it is not currently possible to tell what this altered, presumably strained, conformation is. These studies on RNA model loops are particularly useful for the prediction of RNA secondary structure from sequence (Tinoco et al., 1971), since they provide the first information on the free-energy of loop formation as a function of loop size. Future studies which vary the composition and sequence of the residues in the loop and the helix which closes it should allow greatly improved predictive capacities. This work was supported by grants from the National Institutes of Health (GM10840 and GM41393). We are very grateful to Mrs C. Cech for allowing us to use her thermodynamic data on the AS-GCs-Us loop, and to Mr M. Levine for calculations on the statistical mechanics of the intermediate states model. We are pleased to acknowledge helpful discussions with Mr Levine, Mrs Cech, Mr E. Wickstrom and Miss A. Blum. REFERENCES Allen, F. S., Gray, D. M., Roberts, G. & Tinoco, I., Jr. (1972). Coutts, S. M. (1971). Biochim. Biophys. A&, 232, 94. Davis, R. C. & Tinoco, I. Jr. (1968). Biopolymers, 6, 223.
Biopolymers,
11, 853.
496
0.
C. UHLENBECK
ET
AL.
DeLisi, C. & Crothers, D. M. (1971). l+oe. Nat. Acad. Scci., wash. 68, 2682. Fuller, W. t Hodgson, A. (1967). Nature, 215, 817. Gralla, J. & Crothers, D. M. (1973). J. Mol. Biol. 73, 497. Gray, D. M. & Tinoco, I., Jr. (1970). Biopolymers, 9, 223. Jacobson, H. & Stockmayer, W. H. (1950). J. Chem Phys. 18, 3209. Kallenbach, N. R. (1968). J. Mol. BioZ. 37, 445. Martin, F., Uhlenbeck, 0. C. & Doty, P. (1971). J. Mol. BioE. 57, 201. Romer, R., Riesner, P., Maass, G., Wintermeyer, W., Thiebe, R. & Zachau, H. G. (1969). FEBS Letters, 5, 15. Scheffler, I. E., Elson, E. L. & Baldwin, R. L. (1970). J. Mol. Biol. 48, 145. Tinoco, I. Jr. & Cantor, C. R. (1970). Methods of Biochemicd ktndy8i8, 18, 81. Tinoco, I. Jr., Uhlenbeck, 0. C. & Levine, M. D. (1971). Nature, 230, 362.
Stability of RNA Hairpin Loops : A~-Cm-U, OLKE
C. U~ENBECE~,
PHILIP N, BORER, BARBARA IISNACIO !I’INOCO JR
DEN~LER
AND
Department of Chemistry University of California Berkeley, CaliJ’, 94720, U.S.A. (Received 17 April 1972) The thermodynamics and circular dichroism of a series of A&,-Us (m = 4, 5, 6 or 8) oligoribonucleotides have been studied. These molecules form intramolecular hairpin loops at low temperatures and therefore are useful models for similar structures which occur in larger, natural RNA molecules. The stability of the helix forming the stem of these loops was found to be considerably greater than an intermolecular helix with the same length and composition. The most stable loop is m = 6. The enthalpy for initiation of the loop is unfavorable; it ranges from + 24 kcal. for m = 4 to + 21 kcal. for m = 0. The maximum in stability for the Cs loop and the large positive enthalpy for loop initiation are in disagreement with expectations from simple theories assuming a Gaussian distribution of end-to-end distances. Loop strain for m = 4 and m = 5 and the unstacking of the cytosines on loop formation are likely physical explanations for these thermodynamic data. The circular dichroism spectrum of cytosine residues in the Cs and Cs loops is very similar to the spectrum of single-stranded oligoribocytidylate. However, the cytosine residues in the Cs loop have a very different circular dichroism spectrum from the corresponding oligo(Cs) spectrum. ‘Tu accordance with the thermodynamic data, we conclude from the circular dichroism data that the Ce loop has an altered conformation from the C, and c,$ loops.
1. Introduction loops are a necessary feature of RNA secondary structure. Whenever an antiparallel helical region is formed by base pairing between complementary sequences of an RNA strand, a hairpin loop must be formed as well. One expects the loop to stabilize its intramolecular helical region relative to an identical intermolecular helix. However, in order accurately to predict a secondary structure on the basis of sequence (Kallenbach, 1968 ; Tinoco, Uhlenbeck & Levine, 1971; DeLisi & Crothers, 1971) it is necessary to have precise thermodynamic information about loop stability. Very few thermodynamic data on loops are presently available. Scheffler, Elson & Baldwin (1970) have studied loops formed by deoxy(A-T) oligomers of various lengths. Loops have also been obtained as fragments of transfer RNA molecules (Romer et al., 1969; Coutts, 1971). It has been difficult to determine from these data (1) the amount which a loop stabilizes its helix and (2) the effect, of the number of residues in the loop on the stability of the helix. In this paper, RNA oligomers of the form A&$,-Us (m = 4, 5, 6 or 8) are studied. It is established that these molecules do indeed form hairpins with a helix of six A-U base pairs and m. cytidine residues in the loop. The thermodynamics of loop Hairpin
t Present 1-.S.A. 33
address:
Department
of Biochemistry, 483
Universit’y
of Illinois,
Urbana,
Ill.
61801,
484
0.
C.
UHLENBECK
ET
AL.
initiation are determined and found to be very different from expected values. The circular dichroism spectra of these molecules also give information about the conformation of the C residues in the loop.
2. Materials and Methods The (A~)~A(pc),,,(pu), oligomers (A&,-U,) were synthesized enzymatically in three steps. First, poly(A) was hydrolyzed, the terminal phosphates were removed with alkaline phosphatase, and the oligomers were separated to obtain A,; second, C residues were added to the 3’ end of As with primer-dependent polynucleotide phosphorylase and the different A&&, oligomers separated; and third, U residues were added to each A-C block copolymer and separated again. The conditions for the f&t two steps were identical to those described by Martin, Uhlenbeck & Doty (1971) for the synthesis of A,-TJ,, except that CDP was used instead of UDP. The addition of U residues to A&&,, was done under the following conditions: 0.54 mM-As-C,, 17 mM-[3H]UDP (5.7 Ci/mole), 0.01 M-MgCl,, 0.6 an-NaCl, 0.2 M-&C&! buffer (pH 9.3) and 0.3 mg/ml. concentration of primer dependent polynucleotide phosphorylase from M. luteua. The reaction was run at 37°C for 2 hr. Unfortunately, the A& reaction mixture was lost and has not been repeated yet. Reaction products were separated on a 50-ml. TEAE-cellulose column at pH 3.5 in 7 M-urea. The reaction mixture was diluted with 7 M-urea to an ionic strength of 0.02 M and applied to the column at neutral pH. The unreacted UDP was usually eluted from the column with 0.05 M-Nacl, 0.01 rd-Tris in 7 M-Urea at pH 8. Then the column was equilibrated with 0.01 M-sodium formate, 7 M-urea (pH 3.5) and the oligomers were eluted with a gradient (900 ml. total volume) from 0 to 0.275 M-NaCl in 0.01 m-sodium formate, 7 M-urea (pH 3.5). The elution profile for A&&-UN is shown in Fig. 1. Fractions were pooled and desalted as described in Martin et al. (1971). Identification of the reaction products was accomplished by two methods. First, the specific activity of each peak could be compared with the fraction of U residues in the molecule and second, early peaks could be hydrolyzed with RNase A, chromatographed on paper to separate U and Up, and the radioactive Up/U ratio determined, thus giving the chain length (Martin et al., 1971).
Bm. 1. TEAE-cellulose colunm elution profile of A&U, oligomeru. The large first peak (2) contains N = 0, 1 and 2 as well as some of the UDP. The succeeding peaks me the A,C,UN series starting with N = 3. (SW text for chromatogmphic details.)
STABILITY
OF RNA
HAIRPIN
LOOPS
486
(b) Measurements Absorption-temperature profiles were measured on an automatic recording spectrophotometer (Gilford Instruments) es described in Martin et al. (1971). The solvent consisted of 1 M-NaCI, 0.01 ~-sodium phosphate buffer, and lo-* M-sodium EDTA, adjusted to pH 7. Ultraviolet absorption spectra were obtained with a Gary no. 14 spectrophotometer equipped with a thermostatically controlled circulating block. Circular dichroism spectra were taken with a Cary no. 60 spectropolarimeter with a model 6001 accessory. A PDP S/S computer wae used for on-line data acquisition and reduction (Tinoco & Cantor, 1970). The temperature was controlled by a thermostatically controlled thermoelectric cooler (Allen, Gray, Roberts & Tinoco, 1972). The spectra are presented ae either circular dichroism (cn - cs) or ellipticity per mole of base. Extinction coefficients were obtained by alkaline hydrolysis of the oligomer. The values obtained for l zeo at 47% of A&&-Us are 9.3, 9-3, 9.1, 9.0 ( X 103) lmole-lcm-l for m = 4, 5. 6 or 8, respectively. (c) Treatmerrt of melting d&u The absorbance-temperature profhes of the loop to coil transitions of the A&&-U, oligomers represent a sum of (1) the change in absorbance of the A*U double helix melting; (2) the change in absorbance of the C residues se the loop becomes a single strand; and (3) the change in absorbance of the single strand with temperature. It is therefore not possible to evaluate the absorbance-temperature profile ae a helix-oil transition unless certain assumptions and corrections are made. Figure 2 summarizes the conversion of a melting curve to a plot of fraction helix verau.s temperature. The melting curve, A(T), can be corrected for single-stranded unstacking by using the absorbance change accompanying this unstacking, A,(T), as the upper bound of the melting curve (Martin et al., 1971 and Fig. 2(a)). As(T) can be measured by melting at very low salt ooncentrations, where no helix is formed or it can be calculated from the unstacking of the component residues. The absorbance of the fully formed loop, A,(T), is more diflicult to obtain. In all the loops studied, the transition was quite broad and occurred at such low temperatures that
Temperature
(“Cl
FIQ. 2. (a) Absorbance-temperature profile of AB-C&-U6 in 1 n-N&l, 10 mn-sodium phosphate (pH 7) normalized to 1.0 at 60°C and an average of five different concentrations. A,(T) is the absorbanoe of the oligomer as a single strand. AD(T) is the absorbanoe of the fully formed loop extrapolated to 0 slope in method 1 and to a slope corresponding to oligo (C) unstaoking in method 2. (b) Fraction of loop vef%?u8 temperature for A~-CB-UBcalculated from (a) by methods 1 and 2.
486
0.
C. UHLENBECK
El’
-11,
at 0°C the loop was uot fully formed. Thus, A,(T) must be obtuiuod by extrapolation. Furthermore, since the conformation of the C residues within a closed loop may change with temperature, A,(T) might change with temperature. In order to obtain a reliable estimate of AL(T), the slope of A(T) is plotted as a function of temperature and extrapolated to low temperature. One can extrapolate to zero slope and choose A,(T) as independent of temperature and equal to the extrapolated absorbance. This is method I shown in Fig. 2. Alternatively one can assume that the C’s in the loop change their absorbance with temperature as much as single-stranded oligo (C) does. In this case (method 2) A,(T) is extrapolated to a final slope of O.2o/o/1O deg. C. For both methods, the frection of loop, f, is then calculated as :
43(T) - A(T) f = A,(T) - A,(T). In Fig. 2(b), f ver8u9 T is given for the two alternative methods of estimating A,(T). Only a few degrees difference in the T, (f = 0.5) and a small change in the slope is observed. We will baee the results on method 1, a constant value of AL( T), for simplicity. An alternate method of evaluating T, is to equate it to the maximum in slope of the measured absorbance (dA/dT) max. This method led to higher values of T, than reported here. However, it did not give an internally consistent pattern of results and there is no theoretical reason why the maximum in slope of absorbance should occur at f = O-5 for a multistep equilibrium.
3. Thermodynamic
Results
(a) Single strand to complete loop We want to study the thermodynamics of formation loops. The complete reaction can be written as A,-C&U,
(single strand) + A&&-U,
of intramolecular
hairpin
(loop)
with equilibrium constant equal to f/( 1 - f) where f is the loop fraction. The thermodynamic parameters which characterize the reaction are : T,, the temperature where f = 0.5 (the equilibrium constant = 1); AH0 (total), the standard enthalpy of the reaction; AX0 (total), the stands,rd entropy of the reaction. The value of AH0 (total) can be derived from the van? Hoff equation.
AH0 (total) = 4RT& (aflaT),,.
(1) This form is used because the value of the slope (aflaT) is most accurate at T, where it is least affected by assumptions about extrapolated low and high temperature values for absorbance. This relation will underestimate the value of the total enthalpy if the reaction is not a two-state equilibrium as shown. The standard free energy, AGO,equals 0 at T,, so the standard entropy is given by:
AS0 (total) = AH0 (t&1)/T,.
(2)
Since both the loop to single strand transition and the unstacking of single strands are intramolecular reactions, the absorbance versus temperature profiles of the loops should be independent of concentration. Thus, for each A,-C,-Us (m = 4, 5, 6 or 8) at least four absorbance veTsu.9T curves were obtained over a 25-fold range of oligomer concentration. In each case, the normalized absorbance curves were independent of concentration to within experimental error. We concluded that only intramolecular loops formed and we averaged the data for the different concentrations. Further evidence for the formation of double-stranded intramolecular helices came
STABILITY
I 01’
OF
RN.4
H.1IRI’IN
-.------
b
-10
IO
LOOT’S
20
30
Temwrotwe
40
i
b0
5G
(“Cl
FIG. 3. Loop fraction vws’8u8temperature for As-&,-Us wz == 4,5,6 or 8 in 1 M-NaCl, 10 mm-sodium phosphate (pH 7) calculated by method (1). Each curve is an average of at least four different oligomer concentrations. The dotted lines indicate extrapolation of low temperature data.
from the ultraviolet spectra of the loops. The spectral changes on melting of A,C,-U, were consistent with double-strand melting, while for oligomers with more than six uridines, the spectral change is characteristic of triple-strand formation, suggesting multistrand aggregates (Martin et al., 1971). If the absorbance of the completely formed loop is assumed to be independent of temperature (method l), the f versus T curves thus obtained for the four oligomers are shown in Figure 3. The thermodynamic parameters obtained from these curves are given in Table 1. (b) Loop initiation To learn about the process of closing the loop by the formation of the first base pair, we must consider the single strand to loop reaction in more detail. The simplest TABLE 1
Experimental thermodynamic parameters for the reaction A,&‘,,,- U, (sin~glestrand) to A,-C,-U, (loop) Loop
Tm (“‘3
&CaUfi
2 13.4 21.0 13.4
A&Us AeCeU, AeCsUe t The percentage
AH0 (total) (kcal./mole)
is calculated
O/h = 1oo x As (SO’C) - AL (--10°C) 0
As(60"C)
‘WI
(4 -- 44 -46 -54 -61
-12 -13 -16 -14
hyperchromioity
ASP (total)
17 19 17 19
at 60% as
*
0.
488
C. UHLEKBECK
E’T
AL.
(all or none) assumption is that the reaction takes place in one step, and that the equilibrium constant for the reaction of A,-C,-U, can be written as f y-q
=
YllP
N-l
where y,,, is the equilibrium constant for loop initiation for a loop of VL unbonded bases and s is standard notation for the equilibrium constant for adding each successive base pair to an initiated helix. Both s and Y,,, are expected to be temperature dependent. s(T) = exp [-(dRO/R)(g
24&J
= ymWexp
- &)I
[--(dH9IR)(~
,
- $1
.
In the equation for s(T), Tz is defined as the temperature where s = 1. For the A-U base pairs in A,-C,-U, this is equal to the T, for poly(A)*poly(U) at the same salt concentration. The standard enthalpies which appear in the equations are: AH,O, enthalpy of loop initiation, and Al?O,enthalpy (per base pair) of helix propagation. For simplicity the enthalpies are chosen independent of temperature, although in general they should also vary with temperature. Applying the van% Hoff equation, that is, taking the derivative of the equilibrium with respect to temperature, we obtain
1
1
R (N - l)AHi” In Ym(Tm)
for the relation between melting point for the loop, T,, and thermodynamic parameters. This equation differs from that given by Kallenbach (1968) by the appearance of (N - 1) instead of N. He chooses the equilibrium constant for loop initiation to be proportional to a; this leads to (N)Al?O. We follow Scheffler et al. (1970) in the definition of ym; they discuss its advantage. Tg and AR0 can be obtained directly from experiments on poly(A).poly(U). AR0 can also be calculated from thermodynamic data on the melting of self complementary oligomers of the type A,-U,. In 1 M-N&~ we use: Tz = 78°C and AR0 = -8.0 kcal./mole (Tinoco et al., 1971). When these values and the measured T, for each oligomer are substituted into equation (4), one obtains y,,, values for the four loops at their T,. The enthalpy of initiation, AHlo, for these oligomers can be obtained by subtracting (5)( -8.0) = -40 kcal./mole from the enthalpy of the total reaction given in Table 1. AHi can then be used to calculate y,,, at 26°C from y,,, at T, by equation (3). The y,,, (25°C) and the corresponding free energies and entropies of initiation at 25°C are given in Table 2. Data are also available for a loop with an altered stem (C. Cech, unpublished work). The loop formed by As-G-C&-U, is similar to the A,-C!,-Us loop except that the base pair closing the four rmbonded cytosines is a G*C pair instead of an AmU pair. The T, of As-G-C&-U, is 19.7% and its total AH0 = -15 kcal./mole. The fact that this T, is nearly 18 deg. C higher than the T, for A,-C,-U, is not surprising in view of the fact that the A,-G-C&-U, stem contains 16.7% G-C base pairs. Using equation (4) with Tg adjusted to 90°C to account for the higher G-C content, we obtain y,,,
STABILITY
OF RNA
HAIRPIN
489
LOOPS
TABLET Calculated thermodynamic parame&rs at 25°C for form&q the jirst A- U base pair which chxes a loop of C residues All-or-none No. of bases in loop (m) 4 5 6 8
Ym
0*7x 1.6 x 2.6x 1.4x
10-e 10-e 1O-5 10-S
model
AH,O (kcal./mole)
AS,0 (eu)
AB,O (kcal./mole)
+2s
+70 +@J +59 +65
+7*1 +6.6 +tG3 +6*6
+27 +24
+26
Model with intermediate No, of bases in loop (m) 4 5 6 8
Ym
0.3 x 0.9 x 2.0x 1.1 x
10-B 10-s 10-5 10-E
states
AH,O (kcal./mole)
AS,O (eu)
A&O (kcal./mole)
+24 +24
1-55 -1-57 +49 -t 68
+7*5 $6.9 +6.4 $6.8
+21 +24
(25’C) = 0.5x 10-5, AC,0 = $7.3 kcal., ARio = $25 kcal. and AS,0 = +59 eu. These values are very similar to those given in Table 2 for A6-C4-U6. Up to this point, the thermodynamics of loop formation has been discussed in terms of a simple two-state model. Although it seems intuitively reasonable that this approximation is valid for loops containing only a few base pairs, it is important to test the validity of the approximation by computing the thermodynamics with a more rigorous model. Thus, a partition function which contains all the likely partially bonded intermediate states was derived; the contribution of each intermediate state to the absorbance was assessed; and the effective fraction of base-paired states was calculated (M. D. Levine, unpublished work). In this formulation, a statistical weight of 1 WESassigned to the single strand. All possible loop sizes were considered for the partially bonded states. That is, for A,-C,-U, loops of m, m + 1, m + 2 . . . m + 2N - 2 unbonded bases were counted as intermediate forms. In other words, not only could melting occur from either end of the helix, but staggered conformations with tm uneven number of A’s and U’s in the loop were allowed. However, interior loops and “bulges ” in the helix were excluded as they can easily be shown to be negligible for a helix which can at most contain six base pairs. The contribution of each intermediate state to the change in absorbance was assumed to be proportional to the number of base-pair stacking interactions. A nearest-neighbor approximation of this sort has been found to be applicable in many related contexts (Gray & Tinoco, 1970). The effective fraction of base-paired states could then be calculated as a function of temperature with y,,, and AHi as variable parameters. AB” was chosen equal to -8-O kcal., as before. Unlike in the all-or-none model, the parameters for each oligomer depend on all the other oligomers. For example, to calculate a melting curve for A&&-U, all possible loop sizes from the minimum loop of four unbended bases to the maximum loop of 14 unbonded bases must be considered. That is, the
490
0.
C. UHLENBECK
ET
AL.
values of y4, ys . . . y14 must all be specified. However, in this case, t,he most important variable is y4 corresponding to the actual number of residues in the fully formed loop. The other values of y,,, are used to calculate the intermediate, partially paired forms. Values of y,,, for m > 8 were calculated from Ys+s
-=
9
a/=
( 9t-2 > * This is the chain-length dependence for ym predicted for a single strand which has a Gaussian distribution of end-to-end distances (Jacobson & Stockmayer, 1950). The values for AH,O for m > 8 were set equal to AH,O(m = 8). y7 and AH,O(m = 7) were chosen as the average of the corresponding values for m = 6 and m = 8. The values of the thermodynamic parameters at 25°C obtained from fitting the calculated values (by the complete partition function) of T, and (df/dT) Tmto the measured values are given in Table 2. The values are not too different from those obtained from the all-ornone model; however, the partition function shows that intermediate species are significant. This is particularly true for A&,-U, and A&,-U, where one base pair can break to produce a more favored loop. Y8
4. Thermodynamic
Discussion
The best way to discuss the results of the thermodynamic analysis of loop closure is in the context of what one should expect. For a flexible chain the probability of loop closure should increase as the chain length decreases. Ideally, this should continue until some minimum loop size is reached. Since model building indicates that the minimum loop size is three unbonded bases for polyribonucleotides, we expect y,,, to increase as m decreases, with y3 a maximum. The simplest theory of loop initiation based on a “random coil ” single strand (Jacobson & Stockmayer, 1950) predicts in fact that y,,, should be proportional to (m + 1)-3Ja. The only previously measured value for ym is that of y4 = 30 x 10m5by Scheffler etal. (1970) for deoxy(A-T) oligomers in 0.5 M-Na + . They assumed that the value was independent of temperature, that AHi was zero. It does indeed seem reasonable for AH,O to be zero or plus or minus 1 or 2 kcal., if the enthalpy of initiation is a result of forming two hydrogen bonds (one base pair) in aqueous solution in a completely flexible loop. The experimental thermodynamic results are gathered in Tables 1 and 2. We immediately note that the measured T, values, and therefore the calculated yrn values, do not increase monotonically with decreasing numbers of C’s in the loop. Although the T, for the CC loop is greater than that of the C, loop, the T, values of the C4 and C, loops are less than the C, loop instead of more. Furthermore, the value of y4 calculated with the complete partition function is l/100 the value of y4 for the deoxy(A-T) oligomers. The ym values are also very temperature dependent; the AHi values are over 20 kcal. Finally, the free energies of initiation, which range from f7.5 to +6*4 kcal./mole are somewhat higher than expected (Tinoco et al., 1971; DeLisi & Crothers, 1971). However, DeLisi & Crothers (1971) did calculate that a loop of five unbonded bases should be slightly more stable than one of four unbonded bases. It is also rather remarkable that the ASi displayed in Table 2 have such large positive values. The large entropy increase upon forming a more ordered structure apparently reflects a favorable change in wat,er structure.
STABILITY
OF RNA
HAIRPIN
LOOPS
491
The discrepancy between the measured values and trends for AG,O, AH,0 and AX,O and the simple theoretical estimates can be attributed partly to unstacking of cytosines when the single strand is bent into a loop. If the temperature dependence of the optical rotation of CpC is analyzed in terms of a two-state stacked or unstacked model, approximate values of AH0 (unstacking) = +7 kcal. and AS0 (unstacking) = 25 eu are obtained (Davis & Tinoco, 1968). Therefore, independent of the size of the loop, the values of AHi and AXi in loop initiation are consistent with loss of about three CpC stacking interactions. Thus, either all the cytosines in the loop are partially unstacked or two cytosines are completely unstacked. Studies with molecular models of loops with four to eight unbonded bases indicate that both these possibilities could occur. A model of a loop of seven residues in which two of the bases are completely unstacked and the other five are fully stacked has been carefully described by Fuller & Hodgson (1967). These results imply that the stability of a loop can depend on the base composition and sequence of the residues in the loop as well as those which close it. Uracil, which essentially does not stack, should be particularly important. RNA loops with only A, C, or G in them probably show similar behavior to the C-containing loops studied here. Loops which contain U (particularly next to the helical region as in anticodon loops) may have smaller y,,, and AHi values near zero. These loops could be more reasonably compared with the theoretical estimates of AG,O which ignore basebase interactions. The recent work on A,-G-C&U4 hairpin loops by Gralla & Crothers (1973) made us reassess carefully our methods and results. We conclude that our experimental results are essentially consistent with theirs; our analysis is different. We try to est)imate the fraction of loop (f) versus T by making reasonable assumptions about the absorbance of the oligonucleotide. Once f is obtained, our thermodynamic analysis is straightforward and gives T,(f = 0.5) and AG,O, AH,O and AS,O. Gralla & Crothers do not attempt to make assumptions about absorbance. They equate T, to the maximum in the slope of absorbance verse T and they assume that AHi = 0. In an attempt to get agreement with Gralla & Crothers we assumed a very large variation in absorbance of the completely formed loop with temperature A,(T). This led to enthalpies for loop initiation (AH,O) of about $10 kcal. We could not make our data consistent with AH,O = 0.
5. Circular Dichroism The circular dichroism spectrum was measured for each of the A&,-U, as a function of temperature in 1 M-N&I at pH 7. The spectrum of each oligomer at 0°C is shown in Figure 4. However, even at 0°C these oligomers are not all in one conformational form. The fraction of helix varies from 0.54 for A,-C?,-U, to 0.87 for As-C&U,; this makes the spectrum quite complex and difficult to analyze. Thus, the 0°C spectrum is a mixture of the spectra of single strands, of the fully formed loop and, if intermediate states are important (as deduced from the partition function), of loops with incompletely formed helices. When temperature is increased, the proportions of these different forms change and a corresponding circular dichroic spectral change is seen. In Figure 5 the spectrum of A,-C&Us is shown at four temperatures spanning the transition range. As was the case for the absorption-temperature studies, the differences between the low and high-temperature circular dichroism spectra are due to (a) the change due to the A*U pairs breaking, (b) the change due
0.
492
/
i8
C. UHLENBECK I
I
ET
AL.
I
I
I
Wavelength
(nm)
I
I
..‘..“..
A6- C&
fLoop =O-77
---
Ag-Cg-Ug
fLoop =0,87
-- -- - -
A’6-Cg-Us As-L-U6
fL,,p ~0 74 fLoop =0,54
I
(6
I
with m = 4,6,6 or 8 in 1 M-N&I, 10 rnM-sodium FIQ. 4. Circular dichroism spectra of A,-C,-U, phosphate (pH 7) at 0°C. The fraction of fully formed loop (f) for each oligomer is shown in the Figure.
T !61-
I
I
I
-__
14.--I
-61
I
0°C !=087 Q-yCfz, 60°C f q OOl
’
I
220
I
I
240
I
I
Wavelength FIQ.
6. Circular
diohroism
I
260
I 280
I
I 300
I-2
inm!
of A&&U8
at 0, 20,40 and 60°C.
to unstacking of the single strands with temperature, and (c) the change accompanying the unstacking of the C residues when the loop is formed. The circular dichroism spectrum can be used to give qualitative information about the residues in the loop if we assume that the value per base of the A,*U6 stem can be estimated from circular dichroism measurements of double-stranded A*U base pairs. In the simplest method, we assumed that the spectrum of the cytosine residues in a loop can be obtained by subtracting the spectral contribution of the A-U stem from the total spectrum of the loop. The A-U contribution at different values off was obtained from measured circular dichroism spectra of A,-Ue at the same value off. The double helix formed by A,-Us was chosen as a model for the stem region of the
STABILITY
OF RNA
HAIRPIK
LOOPS
493
loop because, as an oligomer, it probably corresponds more closely to the conformation of the stem region than does the double-stranded polymer poly(A) *poly(U). Furthermore, A,-U, melts over a sufficiently wide range to obtain spectra at various values of j. Oligomer mixtures of A, and U, tend to form triple-stranded aggregates in high salt concentrations and thus are not suitable models. We therefore measured the circular dichroic spectrum of an A,-C,-U, loop at various temperatures (corresponding to different j values) and subtracted the correct molar proportion of the A,-U, spectrum measured at the same value of j. In the A,-C,-U, case, the absorbance-temperature profile is similar to that of A,-U, so the contribution of singlestrand stacking to the difference spectrum is quite small. The total contribution of the A-U residues is thus removed from the spectrum even though they are partially paired and partially single-stranded. Single-strand stacking appears more in the subtractions for the other loops since the temperature of the A,-Uc spectrum must be higher for these less stable loops. This difficulty is most serious in the case of A&7,-U, where, for example, an A,-U, spectrum at 25°C (j = 0.54) must be subtracted from the 0°C loop spectrum (f = 054). In Figure 6(a) and (b), the spectrum
1'
-I-, 22 20
/i:
_ (b)
18 16 14 12 IO 8 6 4
Wavelength
( nm i
FIN. 6. Three times the circular dichroism of A&&,-U6 minus twice the spectrum of Ae-U,, at (a) f = 0.87 (OV for loop) and at (b) f = 0.14 (4O’C for loop) compared with the spectra of Cg at 0 and 40°C.
PO.1
0.
C. UHLENHECK
E7’
;il;.
of the cytosines in the C, loop of A&&-U, at O’C are compared with the measured spectra of the oligonucleotide (Cp)& The comparison is made at 0°C and 40°C corresponding to f values of 0.87 and 0.14 for the loop. Three points should be noted. First, there is excellent agreement of the general shape of the calculated spectrum of the C residues in the loop and the measured oligo(C) spectrum. This suggests that the loop C residues are in an average conformation not radically different from what, they are in single-stranded oligo(C). The second point is that the calculated circular dichroic spectra of the C residues in the loop change with temperature, implying t,hat these residues are quite free to move while in the loop. Finally, the intensity of the calculated spectra is always somewhat greater than the corresponding measured oligo(C) at the same temperature. Although this may imply that C’s in the loop have more structure than in the single strand, the many assumptions involved in the subtraction make quantitative conclusions suspect. An attempt to improve the calculation of the spectra of the loop residues was made by assuming nearest-neighbor interactions for the A*U interaction in the center of A,-U, and for the A-C and C-U interfaces between stem and loop. We correct for the fraction of single strand by subtracting an appropriate amount of the circular dichroism of the oligonucleotide C,. This leads to a very similar shape and about a 5% increase in the maximum at 275 nm. Thus, no significant change from the simpler method is obtained. When the calculation of the circular dichroic spectrum of C residues in the loop is made for the other A&,-U, loops, an interesting observation is made. For m = 8 the spectra are essentially the same as for m = 6, but for m = 5 the calculated spectra differ considerably in position and magnitude from the corresponding oligo(C) spectra. Figure 7 shows the contribution of the C residues in the loop for A,-C&-U, and A,-C&-U, at 0°C. These molecules both have about 75O/, helical structure at 0°C and are directly comparable. A similar comparison with the C, loop is not expected to be accurate since A,-C,-U, is only 54% helical at O”C, leading to a large contribution from single-strand stacking in the difference spectrum. The circular dichroism
240
260
280
300
320
Wavelength (m-n)
FIG. 7. Calculated ciroular diohroism spectra of loop cytosines in A@-CS-UB at 0°C (f = 0.77). The appropriate amount of the diohroism of A,-UB at the same fraction helix is subtracted as in Fig. 6.
STABILITY
OF
RNA
HAIRPIN
LOOPS
-195
data imply that the C, loop has an altered conformation from the C6 and C, loops. This is consistent with the anomalously low stability found for C, and C, loops.
6. Conclusion The RNA hairpin loops studied in this paper are of the same size range as those believed to occur in natural RNA’s. Although the sequence of residues in the model loops could not be considered very natural, the information obtained from these molecules is probably quite applicable to their biological counterparts. The stability of the helical region closing the model loops was studied in detail. As was expected, the entropic effect of restraining complementary sequences to be close to one another did much to stabilize the helix. In our case, the T, of two complementary strands with six A.U base pairs has been estimated to be -13°C at 10m4 M strand concentration (Martin et al., 1971), while the T’, of the loops are in the range of +lO”C at all strand concentrations. The most striking result of the stability measurements was that the six-membered loop was the most stable. Smaller loops were strained and larger loops showed the expected decrease in stability due to decreased probability of the A, and U, regions meeting. We note, of course, that two of the three loops in the well-described cloverleaf model of transfer RNA always have seven residues. Unfortunately, we did not measure a loop with seven bases, but we are confident that such a loop will have near maximum stability. Little can be said about the conformation of the residues in the loop. The high free-energy of initiation of the first helix base pair suggests that either total unstacking of two loop residues or partial unstacking of all the residues must occur before the loop can form. This conclusion should be checked with loops which have U residues in them and therefore do not stack well, or with loops melting at higher temperatures in which the loop bases unstack before the loop melts. The circular dichroism studies suggest that the average conformation of the C residues in the unstrained loops is not significantly different from the average single-strand conformation of oligo(C) residues. The measurements are not sensitive enough to confirm the unstacking predicted by the thermodynamics. The average conformation of the C residues in the loop A&,-U, apparently is different from As-Cs-Us, A,-C&-U,, and oligo(C), since the calculated circular dichroism spectrum is considerably different. We expect similar behavior in the C, loop, but it is not currently possible to tell what this altered, presumably strained, conformation is. These studies on RNA model loops are particularly useful for the prediction of RNA secondary structure from sequence (Tinoco et al., 1971), since they provide the first information on the free-energy of loop formation as a function of loop size. Future studies which vary the composition and sequence of the residues in the loop and the helix which closes it should allow greatly improved predictive capacities. This work was supported by grants from the National Institutes of Health (GM10840 and GM41393). We are very grateful to Mrs C. Cech for allowing us to use her thermodynamic data on the AS-GCs-Us loop, and to Mr M. Levine for calculations on the statistical mechanics of the intermediate states model. We are pleased to acknowledge helpful discussions with Mr Levine, Mrs Cech, Mr E. Wickstrom and Miss A. Blum. REFERENCES Allen, F. S., Gray, D. M., Roberts, G. & Tinoco, I., Jr. (1972). Coutts, S. M. (1971). Biochim. Biophys. A&, 232, 94. Davis, R. C. & Tinoco, I. Jr. (1968). Biopolymers, 6, 223.
Biopolymers,
11, 853.
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0.
C. UHLENBECK
ET
AL.
DeLisi, C. & Crothers, D. M. (1971). l+oe. Nat. Acad. Scci., wash. 68, 2682. Fuller, W. t Hodgson, A. (1967). Nature, 215, 817. Gralla, J. & Crothers, D. M. (1973). J. Mol. Biol. 73, 497. Gray, D. M. & Tinoco, I., Jr. (1970). Biopolymers, 9, 223. Jacobson, H. & Stockmayer, W. H. (1950). J. Chem Phys. 18, 3209. Kallenbach, N. R. (1968). J. Mol. BioZ. 37, 445. Martin, F., Uhlenbeck, 0. C. & Doty, P. (1971). J. Mol. BioE. 57, 201. Romer, R., Riesner, P., Maass, G., Wintermeyer, W., Thiebe, R. & Zachau, H. G. (1969). FEBS Letters, 5, 15. Scheffler, I. E., Elson, E. L. & Baldwin, R. L. (1970). J. Mol. Biol. 48, 145. Tinoco, I. Jr. & Cantor, C. R. (1970). Methods of Biochemicd ktndy8i8, 18, 81. Tinoco, I. Jr., Uhlenbeck, 0. C. & Levine, M. D. (1971). Nature, 230, 362.